Can I create an OpenGL 1.1 game on Blender 2.78 32-bit Game Engine?
The BGE runs on 


Windows, 
MacOS, 
Linux.


Nintendo, PS2, Mobile phones do not run that platforms. So you can't use the BGE there even if there is a matching OpenGL support. (OpenGL is another requirement, not the only requirement)


  I want to create a game that can possibly be ported to Kivy or Unity which can be ported to other systems


I'm not sure how you interpret porting a game to another platform or to use different frameworks. You basically develop a completely new application that feels like the original one. So the "business" stays the same while the application is completely different. 

It is nothing ...


  for learning how to script or create games


If the question in your mind is meant to be:


can I create BGE games on my mobile phone? the answer is no.
can I run my BGE game in my mobile phone? The answer is no.
can I transfer my BGE skills to other game engines that run on mobile phones? The answer is ... some of them:


concepts of game development. 
scripting? 


general concepts - yes
specific code - no
specific methods - not likely




[Edit]


  Can I create an OpenGL 1.1 game on Blender 2.78 32-bit Game Engine?


I can't tell. Accoring to this question Blender 2.77+ needs OpenGL 2.1. I have no idea if that is compatible with OpenGL 1.1.

The supported OSes remain the same as mentioned above (WinOs, MacOs, Linux).

You might try it out by setting up a Linux with OpenGL 1.1 only.